使用TensorFlow的线性回归
本教程是关于通过TensorFlow训练线性模型以适应数据。或者,您可以查看此博客文章。
介绍
在机器学习和统计中,线性回归是对诸如Y的变量和至少一个自变量之间的关系的建模为X.在线性回归中,线性关系将由预测函数建模,其参数将被估计通过数据并称为线性模型。线性回归算法的主要优点是其简单性,使用它可以非常直接地解释新模型并将数据映射到新空间。在本文中,我们将介绍如何使用TensorFLow训练线性模型以及如何展示生成的模型。
整个过程描述
为了训练模型,TensorFlow循环遍历数据,它应该找到适合数据的最佳线(因为我们有一个线性模型)。通过设计适当的优化问题来估计X,Y的两个变量之间的线性关系,其中需求是适当的损失函数。该数据集可从斯坦福大学CS 20SI课程 :TensorFlow for Deep Learning Research获得。
代码实现
通过加载必要的库和数据集来启动该过程:
#斯坦福当然CS 20SI提供的数据文件:TensorFlow深学习研究。
# https://github.com/chiphuyen/tf-stanford-tutorials
DATA_FILE = "data/fire_theft.xls"
#从.xls文件中读取数据。
book = xlrd.open_workbook(DATA_FILE, encoding_override="utf-8")
sheet = book.sheet_by_index(0)
data = np.asarray([sheet.row_values(i) for i in range(1, sheet.nrows)])
num_samples = sheet.nrows - 1
#######################
## Defining flags #####
#######################
tf.app.flags.DEFINE_integer(
'num_epochs', 50, 'The number of epochs for training the model. Default=50')
# Store all elements in FLAG structure!
FLAGS = tf.app.flags.FLAGS
python操作excel主要用到xlrd和xlwt这两个库,即xlrd是读excel,xlwt是写excel的库。
然后我们继续定义和初始化必要的变量:
# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")
之后,我们应该定义必要的功能。不同的标签演示了定义的功能:
def inputs():
"""
Defining the place_holders.
:return:
Returning the data and label lace holders.
"""
X = tf.placeholder(tf.float32, name="X")
Y = tf.placeholder(tf.float32, name="Y")
return X,Y
def inference():
"""
Forward passing the X.
:param X: Input.
:return: X*W + b.
"""
return X * W + b
def loss(X, Y):
"""
compute the loss by comparing the predicted value to the actual label.
:param X: The input.
:param Y: The label.
:return: The loss over the samples.
"""
# Making the prediction.
Y_predicted = inference(X)
return tf.squared_difference(Y, Y_predicted)
squared_difference( x, y, name=None)
tf.squared_difference返回(x - y)(x - y)元素.
更多函数建议查W3Cschool-tensorflow
# The training function.
def train(loss):
learning_rate = 0.0001
return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
①tf.train.GradientDescentOptimizer()使用随机梯度下降算法,使参数沿着 梯度的反方向,即总损失减小的方向移动,实现更新参数.
然后使用梯度找到最小train_loss
接下来,我们将循环遍历不同的数据时代并执行优化过程:
with tf.Session() as sess:
# Initialize the variables[w and b].
sess.run(tf.global_variables_initializer())
# Get the input tensors
X, Y = inputs()
# Return the train loss and create the train_op.
train_loss = loss(X, Y)
train_op = train(train_loss)
# Step 8: train the model
for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
for x, y in data:
train_op = train(train_loss)
# Session runs train_op to minimize loss
loss_value,_ = sess.run([train_loss,train_op], feed_dict={X: x, Y: y})
# Displaying the loss per epoch.
print('epoch %d, loss=%f' %(epoch_num+1, loss_value))
# save the values of weight and bias
wcoeff, bias = sess.run([W, b])
在上面的代码中,sess.run(tf.global_variables_initializer())全局初始化所有已定义的变量。train_op建立在train_loss上,并将在每一步中更新。最后,将返回线性模型的参数,例如wcoeff和bias。为了评估,将演示预测线和原始数据以显示模型如何适合数据:
###############################
#### Evaluate and plot ########
###############################
Input_values = data[:,0]
Labels = data[:,1]
Prediction_values = data[:,0] * wcoeff + bias
plt.plot(Input_values, Labels, 'ro', label='main')
plt.plot(Input_values, Prediction_values, label='Predicted')
# Saving the result.
plt.legend()
plt.savefig('plot.png')
plt.close()
摘要
在本教程中,我们使用TensorFlow完成了线性模型创建。训练后发现的线不能保证是最好的线。不同的参数会影响收敛精度。使用随机优化找到线性模型,其简单性使我们的世界变得更容易。
修改后的代码:
from __future__ import print_function
import tensorflow as tf
import os
from tensorflow.python.framework import ops
import xlrd
import numpy as np
# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")
def inputs():
"""
Defining the place_holders.
:return:
Returning the data and label lace holders.
"""
X = tf.placeholder(tf.float32, name="X")
Y = tf.placeholder(tf.float32, name="Y")
return X,Y
def inference(X):
"""
Forward passing the X.
:param X: Input.
:return: X*W + b.
"""
return X * W + b
def loss(X, Y):
"""
compute the loss by comparing the predicted value to the actual label.
:param X: The input.
:param Y: The label.
:return: The loss over the samples.
"""
# Making the prediction.
Y_predicted = inference(X)
return tf.squared_difference(Y, Y_predicted)
# The training function.
def train(loss):
learning_rate = 0.0001
return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
FLAGS = tf.app.flags.FLAGS# Now, the variable must be initialized.
tf.app.flags.DEFINE_string('log_dir', os.path.dirname(os.path.abspath(__file__)) + '/logs',
'Directory where event logs are written to.')
DATA_FILE = "data/fire_theft.xls"
book = xlrd.open_workbook(DATA_FILE, encoding_override="utf-8")
sheet = book.sheet_by_index(0)
data = np.asarray([sheet.row_values(i) for i in range(1, sheet.nrows)])
num_samples = sheet.nrows - 1
tf.app.flags.DEFINE_integer('num_epochs', 50, 'The number of epochs for training the model. Default=50')
with tf.Session() as sess:
writer = tf.summary.FileWriter(os.path.expanduser(FLAGS.log_dir), sess.graph)
# Initialize the variables[w and b].
sess.run(tf.global_variables_initializer())
# Get the input tensors
X, Y = inputs()
# Return the train loss and create the train_op.
train_loss = loss(X, Y)
train_op = train(train_loss)
# Step 8: train the model
for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
for x, y in data:
train_op = train(train_loss)
# Session runs train_op to minimize loss
loss_value,_ = sess.run([train_loss,train_op], feed_dict={X: x, Y: y})
# Displaying the loss per epoch.
print('epoch %d, loss=%f' %(epoch_num+1, loss_value))
# save the values of weight and bias
wcoeff, bias = sess.run([W, b])
writer.close()
另外一个例子:
import numpy as np
import tensorflow as tf
import xlrd
import matplotlib.pyplot as plt
import os
from sklearn.utils import check_random_state
# Generating artificial data.
n = 50
XX = np.arange(n)
rs = check_random_state(0)
YY = rs.randint(-20, 20, size=(n,)) + 2.0 * XX
data = np.stack([XX,YY], axis=1)
#######################
## Defining flags #####
#######################
tf.app.flags.DEFINE_integer('num_epochs', 50, 'The number of epochs for training the model. Default=50')
# Store all elemnts in FLAG structure!
FLAGS = tf.app.flags.FLAGS
# creating the weight and bias.
# The defined variables will be initialized to zero.
W = tf.Variable(0.0, name="weights")
b = tf.Variable(0.0, name="bias")
# Creating placeholders for input X and label Y.
def inputs():
"""
Defining the place_holders.
:return:
Returning the data and label place holders.
"""
X = tf.placeholder(tf.float32, name="X")
Y = tf.placeholder(tf.float32, name="Y")
return X,Y
# Create the prediction.
def inference(X):
"""
Forward passing the X.
:param X: Input.
:return: X*W + b.
"""
return X * W + b
def loss(X, Y):
'''
compute the loss by comparing the predicted value to the actual label.
:param X: The input.
:param Y: The label.
:return: The loss over the samples.
'''
# Making the prediction.
Y_predicted = inference(X)
return tf.reduce_sum(tf.squared_difference(Y, Y_predicted))/(2*data.shape[0])
# The training function.
def train(loss):
learning_rate = 0.0001
return tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)
with tf.Session() as sess:
# Initialize the variables[w and b].
sess.run(tf.global_variables_initializer())
# Get the input tensors
X, Y = inputs()
# Return the train loss and create the train_op.
train_loss = loss(X, Y)
train_op = train(train_loss)
# Step 8: train the model
for epoch_num in range(FLAGS.num_epochs): # run 100 epochs
loss_value, _ = sess.run([train_loss,train_op],
feed_dict={X: data[:,0], Y: data[:,1]})
# Displaying the loss per epoch.
print('epoch %d, loss=%f' %(epoch_num+1, loss_value))
# save the values of weight and bias
wcoeff, bias = sess.run([W, b])
###############################
#### Evaluate and plot ########
###############################
Input_values = data[:,0]
Labels = data[:,1]
Prediction_values = data[:,0] * wcoeff + bias
# # uncomment if plotting is desired!
plt.plot(Input_values, Labels, 'ro', label='main')
plt.plot(Input_values, Prediction_values, label='Predicted')
# # Saving the result.
plt.legend()
plt.savefig('plot.png')
plt.close()
结果如下图所示:
图1:原始数据以及估计的线性模型。
上面的动画GIF显示模型带有一些微小的动作,展示了更新过程。可以观察到,线性模型肯定不是最好的!但是,正如我们所提到的,它的简单性是它的优势!